Dimerization reaction of an α-olefin using a catalyst composed of a combination of a metallocene, an aluminoxane, an organoaluminum compound and the like is publicly known, and examples of such catalyst include a catalyst composed of zirconocene and methylaluminoxane (for example, Patent Document 1), a catalyst composed of zirconocene, alkylaluminoxane, trimethylaluminum (for example, Patent Document 2) and others.
Moreover, oligomerization of an α-olefin is also publicly known, for which a catalyst composed of zirconocene, organoaluminum and borate (for example, Patent Document 3), a catalyst composed of zirconocene, organoaluminum and borane (for example, Patent Document 4), a catalyst composed of zirconocene, methylaluminoxane, and organoaluminum (for example, Patent Document 5), and the like are used.
However, as activity of those catalyst systems are low and a large amount of the catalyst is required, productivity is inferior, and therefore, industrial utilization is difficult.
Furthermore, addition of hydrogen to dimerization and oligomerization reaction systems is not known.
In a polymerization reaction using a metallocene catalyst, hydrogen is added to control the molecular weight of the polymer.
This is to cause chain transfer reaction by the addition of hydrogen, and as a result, terminal groups of the polymer are saturated (for example, Patent Documents 6 and 7).
Therefore, to obtain a polymer having unsaturated double bonds in a high ratio, the addition of hydrogen was considered to be avoided.    Patent Document 1: Japanese Examined Patent Publication No. H07-116065    Patent Document 2: Japanese Patent No. 3073234    Patent Document 3: Japanese Publication of Translation of PCT No. 2002-518528    Patent Document 4: Japanese Publication of Translation of PCT No. 2002-522572    Patent Document 5: Japanese Publication of Translation of PCT No. 2002-522575    Patent Document 6: Japanese Patent No. 3058419    Patent Document 7: Japanese Patent No. 3086469